Incorporating risk into decision-making has been typically carried out by replacing the average utility with the average over a function of the utility [1]}, [2]}.
Examples include a mean-variance tradeoff [3]}, [4]}, [5]}, exponential
utility [6]}, [7]}, [8]}, and conditional value at risk (CVaR) [9]}.
CVaR is the average cost, given that the cost takes sufficiently large values, and has strong theoretical justification for its use [10]}, [11]}, [12]}.
An axiomatic characterization of risk considerations for a robot was presented in [13]}.
Risk-sensitivity has also been represented as a constraint to be satisfied while maximizing an average utility [14]}, [15]}.
Cumulative prospect theory (CPT) [16]} models behaviors of a decision-maker that is risk-averse with gains and risk-seeking with losses, and distorts extremely high and low probability events.
Optimization of a CPT-based cost for MDPs was studied in [17]}, [18]}.
Our previous work [19]} optimized a CPT-based cost in an RL framework, and designed CPT-RL algorithms; a similar paradigm was concurrently proposed in [20]}.
While the above works provide promising solutions for risk-sensitive decision makers, incorporating CPT-based objectives into an RL framework has been relatively less studied.
Further, the consideration of a desire of an RL agent to maintain privacy of its decision making has not been explored using CPT.
